The day before you plan on serving the ribs:
Using a sharp knife, remove most of the thin layer of fat and sinew from the meaty
top of each rib. This will make for a much more elegant presentation later. Season
the ribs with salt and pepper on all sides. Heat all but two tablespoons of the oil in
a large Dutch oven over medium high heat. When hot, add the ribs and brown well
on all sides, including the ends. Don’t crowd the pan, so it will probably need to be
done in two batches. Set the ribs aside for the moment.

Preheat oven to 325 degrees. Lower the heat on the stove top to medium. Discard
the old oil from the pan and add the two tablespoons of reserved oil. Add the onion
and celery and cook until lightly caramelized, about 5 minutes. Add the garlic, stir
and cook for a minute more. Add the flour and stir to incorporate. Add the red
wine and cook a few minutes, scraping up the brown bits from the bottom of the
pan. Then add the thyme, bay leaf, tomato paste, beef stock and the short ribs.
Bring to a simmer and cover the Dutch oven. Place in a preheated 325 degree
oven and cook until tender, about 3 ½ hours. Turn the ribs about half way through
the braising. When the ribs are tender and falling off the bone, gently remove the
meat and bones from the pan using a slotted spoon. Discard the bones and
refrigerate the ribs overnight. Cover only after they have completely cooled. Strain
the braising liquid through a fine mesh sieve into a bowl, pushing down the solids
to get as much liquid as possible. Chill the braising liquid overnight in the
refrigerator, uncovered.

To finish the ribs:
Using your sharp knife again, trim the chilled ribs by removing the fatty, sinewy
part on the bottom that once surrounded the bone. When finished, the ribs will be
completely cleaned for presentation. Set aside. Remove the thick layer of beef fat
from the top of the chilled braising liquid and discard. Now reheat the completely
defatted liquid in a large pan on the stove top. Add the short ribs, cover the pan
and heat through over medium low heat. This will take about fifteen minutes.
Remove the lid and reduce the liquid to sauce consistency. This should only take a
few minutes as the liquid reduced significantly during the braising process. Adjust
the seasoning with salt and pepper.